Robust Stabilization of Linear Switched Systems with Unstable Subsystems
TL;DR: In this paper, the robust stability of a class of uncertain switched systems with possibly unstable linear subsystems is studied. And conditions for global uniform exponential stability are presented. And a procedure to design a mode dependent average dwell time switching signal that stabilizes a switched linear system composed of diagonalizable subsystems, even if all of them are stable/unstable and time-varying (within design bounds).
Abstract: This paper deals with the robust stability of a class of uncertain switched systems with possibly unstable linear subsystems. In particular, conditions for global uniform exponential stability are presented. In addition, a procedure to design a mode dependent average dwell time switching signal that stabilizes a switched linear system composed of diagonalizable subsystems is established, even if all of them are stable/unstable and time-varying (within design bounds). An illustrative example of the stabilizing switching law design and numerical results are presented.
Citations
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26 Nov 2020
TL;DR: In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated, by establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals and adopting a mode-dependent dwell time (MDDT) switching strategy.
Abstract: In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated. By establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals (MCLKF) and adopting a mode-dependent dwell time (MDDT) switching strategy, new delay-dependent sufficient conditions guaranteeing global uniform asymptotic stability of the considered systems are formulated. Apart from past studies that studied switched systems with at least one stable subsystem, in the present study, the MDDT switching technique has been applied to ensure robust stability of the considered systems with all unstable subsystems. Compared with the existing results, our results are more general and less conservative than some of the previous studies. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.
6 citations
TL;DR: In this paper , a robust finite-time control of discrete-time linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is studied, and sufficient conditions containing several symmetric negative-definite matrices are derived to guarantee robust finite time control of the systems.
Abstract: Many practical systems can be modeled in terms of uncertainties, which refer to the differences or errors between actual data and mathematical simulations. However, systems including slight uncertainties and exogenous disturbances may lead to the instability of those systems. Besides, the behavior of systems is preferable to investigate within a prescribed bound over a fixed time interval. Therefore, in this paper, we study a robust finite-time control of discrete-time linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance. A distinctive feature of this research is that the considered systems consist of finite-time bounded subsystems and finite-time unbounded subsystems. A class of quasi-alternative switching signals is validly designed to analyze the mechanism and switching behaviors of the systems among their subsystems. By utilizing a copositive Lyapunov–Krasovskii functional method combined with the slow mode-dependent average dwell time and the fast mode-dependent average dwell time switching techniques, new sufficient conditions containing several symmetric negative-definite matrices are derived to guarantee robust finite-time control of the systems. These results are applied to a water-quality controllability model in streams to the standard level. Finally, the consistent results between the theoretical analysis and the corresponding numerical simulations are shown.
2 citations
TL;DR: In this article , the global stability problem for a class of linear switched positive time-varying delay systems (LSPTDSs) with interval uncertainties by means of a fast average dwell time (FADT) switching is analyzed.
Abstract: The global stability problem for a class of linear switched positive time-varying delay systems (LSPTDSs) with interval uncertainties by means of a fast average dwell time (FADT) switching is analyzed in this paper. A distinctive feature of this research is that all subsystems are considered to be unstable. Both the continuous-time and the discrete-time cases of LSPTDSs with interval uncertainties and all unstable subsystems (AUSs) are investigated. By constructing a time-scheduled multiple copositive Lyapunov-Krasovskii functional (MCLKF), novel sufficient conditions are derived within the framework of the FADT switching to guarantee such systems in the case of continuous-time to be globally uniformly exponentially stable. Based on the above approach, the corresponding result is extended to the discrete-time LSPTDSs including both interval uncertainties and AUSs. In addition, new stability criteria in an exponential sense are formulated for the studied systems without interval uncertainties. The efficiency and validity of the theoretical results are shown through simulation examples.
References
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TL;DR: A sufficient condition ensuring the asymptotic stability of switched continuous-time systems with all modes unstable is proposed, using a discretized Lyapunov function approach in the framework of dwell time.
380 citations
TL;DR: The proposed approach provides a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria, and relies finally on the representability of sampled-data systems as impulsive Systems.
209 citations
TL;DR: A valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability.
Abstract: In this paper, the problem of adaptive neural state-feedback tracking control is considered for a class of stochastic nonstrict-feedback nonlinear switched systems with completely unknown nonlinearities. In the design procedure, the universal approximation capability of radial basis function neural networks is used for identifying the unknown compounded nonlinear functions, and a variable separation technique is employed to overcome the design difficulty caused by the nonstrict-feedback structure. The most outstanding novelty of this paper is that individual Lyapunov function of each subsystem is constructed by flexibly adopting the upper and lower bounds of the control gain functions of each subsystem. Furthermore, by combining the average dwell-time scheme and the adaptive backstepping design, a valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. Finally, the availability of the developed control scheme is verified by two simulation examples.
194 citations
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TL;DR: In this paper, the authors proposed a hybrid framework for stability analysis and control of linear impulsive systems, through the use of continuous-time time-varying discontinuous Lyapunov functions.
Abstract: Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.
155 citations
TL;DR: A new mode-dependent average dwell time (MDADT) switching property is proposed, which is different from the existing one in the literature, and the stabilization condition under such MDADT switching signals is established for the switched nonlinear systems with possibly all unstable subsystems.
Abstract: This paper is concerned with the control problem for a class of switched nonlinear systems possibly composed of all unstable modes by using time-controlled switching signals. To tackle the problem, a new mode-dependent average dwell time (MDADT) switching property is proposed, which is different from the existing one in the literature. Then, the stabilization condition under such MDADT switching signals is established for the switched nonlinear systems with possibly all unstable subsystems. By proposing a class of time-scheduled multiple quadratic Lyapunov function and applying T–S fuzzy models to represent the underlying nonlinear subsystems, numerically easily verified stabilization conditions are further derived in the form of linear matrix inequalities. A numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results.
133 citations